Las creencias de autoeficacia docente y su relación

Stellar X-ray sources, specifically bright XRBs, can be studied out to distances of ∼ 30−40

Mpc with Chandra(beyond this the sensitivity limit is too large and therefore requires pro-

hibitively long integration times). As such most results only sample the high-luminosity end of the XLF (_&1037erg s−1), leaving the low-luminosity end with a flatter slope and ultimately

biased by incompleteness. M31’s X-ray population has been studied in detail byROSAT(Sup-

per et al., 1997, 2001) and XMM-Newton (Stiele et al., 2011). The two deep ROSAT sur-

veys reported 560 total sources while theXMM-Newtondata is much deeper, cataloguing 1897

sources. Each survey was galaxy-wide and therefore allowed the detailed study of a Milky Way analogue below the luminosity of bright XRBs. Interestingly, no HMXBs have been con- firmed yet in M31, stressing the importance of multiwavelength observations in classifying

X-ray sources. Further motivation stems from the 65% of sources in the XMM-Newton sur-

vey that have no classification. The LMXB population has been extensively studied in M31,

particularly in the bulge, where numerous Chandra observations exist. Zhang et al. (2011)

found a different XLF for LMXBs in the bulge and those in GCs, with a break at ≈ 1037 erg

s−1 _{for the XLF of GC-LMXBs. Similar breaks are found for the XLF in the inner and outer}

bulge and disk regions, although the break moves to lower luminosities as radial distance de- creases. Fabbiano (2006b) stressed the need for a comparison of the low-luminosity XLFs in early-type galaxies with those for M31. Kim et al. (2009) addressed this issue by observing 3 old elliptical galaxies and confirming the low-luminosity break in GC-LMXBs compared to

the field sources. Unfortunately the 90% completeness limits are similar to the values for low- luminosity breaks in the GC XLFs. Thus a deeper sample of data that includes more galaxies is necessary to confirm these results.

1.4.2.1 LMXB Evolution

LMXBs dominate the total luminosity of elliptical galaxies in the 0.3−8 keV band, whereas

in NGC 1316 the integrated LMXB emission (including undetected LMXBs) is upwards of

∼4·1040_{erg s}−1_{(Fabbiano, 2006a). The spectra of LMXBs are remarkably consistent through-}

out early-type galaxies with a power law fit having a photon indexΓ ∼ 1.56±0.02. Higher

luminosity sources are better fit with a softer spectrum of Γ ∼ 2. The number of LMXBs is

known to scale with the stellar mass in a galaxy (Gilfanov et al., 2004; Lehmer et al., 2010; Boroson et al., 2011; Zhang et al., 2012b). Zhang et al. (2012a) completed a study of 20 mas-

sive nearby early-type galaxies usingChandrawith over 2000 point sources. They found that

Nx(>5×1037erg s−1)/1010M= 5.4, consistent with the studies mentioned above. In addition,

older galaxies (t > 6 Gyr) tended to host more LMXBs than their younger counterparts, with

an LMXB frequency for LX > 5× 1037 erg s−1 of 6.27± 0.26 and 4.18±0.27 per 1010 M

respectively. They attribute this to the intrinsic evolution of the LMXB population of a galaxy over time, further exacerbated by the presence of more GCs in galaxies with older stellar pop-

ulations. The evolution of the XLF (for log(LX)>37.5) with age showed that younger galaxies

have more bright sources and fewer fainter sources (a flatter slope) than older galaxies.

The consensus within the community is that LMXBs are preferentially found in massive, compact, high-metallicity (redder) GCs that are luminous. The reasons for GC compactness and luminosity as a direct link to the detection of LMXBs is clear from the processes mentioned earlier. Dense clusters promote dynamical interactions triggering binary formation while a larger number of stars would make the GC optically brighter. The metallicity relation, how-

ever, is not as well-understood. In a study of early-type Virgo cluster galaxies, Sivakoffet al.

GCs. Several explanations have been put forth to describe the metallicity relation. Ivanova & Kalogera (2006) posited a process involving magnetic braking in MS stars that would result in the suppression of LMXB formation in metal-poor GCs. Metal-poor MS stars of approxi- mately solar mass lack outer convection zones and subsequently magnetic braking is inhibited, not allowing the orbit to shrink and possibly form a binary. Maccarone et al. (2004) have suggested that irradiation-induced stellar winds (originating from the donor star reprocessing X-ray luminosity from the accretion disk) are stronger in low-metallicity stars because emis-

sion line cooling is not efficient, speeding up the evolutionary process of LMXBs. This would

cause a decrease in the number of observed LMXBs in GCs. Agar & Barmby (2013) conducted a survey of M31 GC-LMXBs and interestingly found the probability that a GC hosts an LMXB had no dependence on metallicity. However, the GC sample had a small galactocentric distance and high average metallicity, possibly biasing the results. The LMXB metallicity relation is clearly still in its infancy and requires more investigation, especially concerning the nature of this dependence in spiral galaxies.

Ivanova et al. (2012) suggests that the metallicity dependence of GC-LMXBs is due to

the differences in the number densities and average masses of red giants in both blue and red

GCs. GC-LMXBs have 3 sub-populations based on the evolutionary state of the companion star: those with MS, red giant, and WD donors. Ivanova et al. (2008) showed that most GC- LMXBs should be accreting NSs. They would be formed mainly through a distinct class of core-collapse supernovae or accretion-induced collapse of a WD. NSs and BHs that are pro- duced via core-collapse supernovae generally all have large enough natal kick velocities (mean

velocity∼ 400 km s−1) due to asymmetric explosion to be ejected from the cluster. The most

efficient formation channel for GC-LMXBs is a NS with a MS donor. This occurs through bi-

nary exchange interaction with a NS or the accretion-induced collapse of an existing WD-MS binary. However, the accretion rates from MS stars are not substantial enough to give X-ray

luminosities above> 1037 _{erg s}−1_{, and thus the sources are transient and have low outburstL}

X

giant donors with higher mass loss rates. Ivanova et al. (2012) found that red giants are on

average larger and more numerous in metal-rich clusters, leading to the observed trend that∼3

times as many bright LMXBs are found in red clusters. Nonetheless, a population synthesis

study incorporating the effects of red giant stars on metallicity is still required.

In a survey of early-type Virgo cluster galaxies with Chandra and HST, Sivakoff et al.

(2007) did not find any dependence on the galactocentric distance to the association of an X-ray source with a GC. At all radii there is a strong dependence of the GC luminosity, com- pactness, and colour. However, a deeper survey of NGC 4278 (Fabbiano et al., 2010) found a

significant radial effect on the luminosity of X-ray sources in GCs, showing a preference for

more luminous sources at smaller radii. The sample consisted of only 7 sources and therefore cannot be considered statistically significant. Similar work considering XRBs in a quiescent state has not been studied to the extent of bright XRBs as a result of observational limits.

1.4.2.2 X-ray Luminosity Function and Star Formation Rate

The correlation between HMXBs and the SFR in spiral galaxies was investigated by Grimm et al. (2003) when they inspected the luminosity function of HMXBs. The much smaller Small Magellanic Cloud had as many identified HMXBs as the Milky Way due to the recent star- formation episode triggered within the past 100 Myr. Even though most galaxies followed a similar curve that declined with increasing luminosity, their values were shifted with respect to each other. By scaling each galaxy with its corresponding SFR, the XLFs overlapped along a single curve to support the correlation of HMXBs as a SFR indicator (Figure 1.5).

The differential XLF from Grimm et al. (2003) in equation 1.4 has a power-law slope ofα

and a normalization constantβ, with L38=L/1038 erg s−1.

dN dL38

=β·SFRLα₃₈ (1.4)

Figure 1.5: Figure 1 from Grimm et al. (2003) showing X-ray luminosity functions of X-ray

sources from late-type and starburst galaxies obtained with Chandra data. On the left the

observed XLFs for various galaxies are shown. On the right the XLF of each galaxy has been scaled by the ratio of its star formation rate to that of the Antennae. Even though the SFRs of

the sample varied by factors∼50 the scaled XLFs reside in a narrow region of theN(> L)−L

plane.

(2003) was recently updated by Mineo et al. (2012). They found the same results for a uni-

versal XLF that was well-fit by a power law with a slope ofα ∼ −1.6, β = 3.3, and a cutoff

at LX ∼ 1040 erg s−1. The normalizations are proportional to the SFR of the host galaxy.

Bulge sources of galaxies with inclination i_.65◦_{were excluded to remove contributions from}

LMXBs that may have skewed their results. The crucial conclusion was that the collective X-ray luminosity of HMXBs (with LMXBs possibly included in the sample) is proportional to the SFR via the relation LXRB_0.5−8keV (erg s−1)=2.61×1039SFR (Myr−1). The scatter in the

LX-SFR relation (0.4 dex) is due to the XLF normalization and the number and luminosity of

the brightest sources. A key driver in the population of HMXBs and ultimately how it influ- ences the XLF is metallicity. Higher-metallicity donor stars will have stronger winds, which subsequently leads to higher (wind) accretion rates and X-ray luminosity of the accretion flow (Linden et al., 2010). However, star formation at low-metallicity does not allow for significant cooling, resulting in the birth of more massive stars and therefore a higher number of compact

objects in binaries. Shtykovskiy & Gilfanov (2005) state that the effects of metallicity varia- tions on XRB populations are poorly understood and require more investigation. Specifically, more detailed analyses of the HMXB-XLF in star-forming galaxies will help to further our understanding of the role of metallicity in relation to XRBs.